Abstract

Many numerical simulation methods, such as finite-element analysis, were originally formulated to run serially or in parallel on central processing units (CPUs). However, computer engineering has seen a paradigm shift toward massive parallelism using graphics processing units (GPUs), which have become the default accelerators in many data-driven scientific disciplines outside of civil engineering. This state-of-the-art review highlights the challenges and practicalities of GPU-accelerating nonlinear dynamic analyses for civil structural problems. To demonstrate the feasibility of a fully GPU-accelerated finite-element analysis, a GPU-based program for linear-elastic dynamic analysis was implemented, where all stages of the analysis were ported to the GPU. Observed speedups were 115 times that of an equivalent CPU-driven analysis for 106 model degrees of freedom (dof). Importantly, the computational time for the assembly and update levels of the analyses were nearly independent of the number of dof. High-resolution simulations of complex structures can be computationally expensive, but these results and advances in other fields suggest that some levels of the finite-element analysis of civil structures could be accelerated using GPUs at increased model resolution with little increase in computational cost, demonstrating the potential for GPU-accelerated computing. However, compared to other GPU-accelerated finite-element analysis applications, the dynamic analysis of civil structures is subject to unique challenges that need to be addressed before GPU acceleration can be fully realized. Aspects of simulating the response of civil structures considering nonlinear response under extreme loading may not be immediately amenable to GPU acceleration; e.g., the use of many differing element formulations within a model, potential for inelastic response and varying degrees of nonlinearity across elements, and traditional reliance on implicit integration schemes with direct solvers. The shift to GPUs is part of a larger movement toward specialized hardware using fine-grained parallelism, and structural engineers need to address these challenges as these emerging technologies become more prevalent.

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Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon request.

Acknowledgments

This research was supported by National Science Foundation (NSF) under grant number CMMI-2145665, titled CAREER: Accelerating Real-time Hybrid Physical-Numerical Simulations in Natural Hazards Engineering with a Graphics Processing Unit (GPU)-driven Paradigm. Special thanks to Dr. Frank McKenna for providing feedback on the initial drafts of this paper. The findings, opinions, recommendations, and conclusions in this paper are those of the authors alone and do not necessarily reflect the views of others, including the sponsors.

References

Alexander, F., et al. 2020. “Exascale applications: Skin in the game.” Philos. Trans. R. Soc. A 378 (2166): 20190056. https://doi.org/10.1098/rsta.2019.0056.
Amdahl, G. M. 1967. “Validity of the single processor approach to achieving large scale computing capabilities.” In Proc., AFIPS Conf. Proc., 483–485. Reston, VA: American Federation of Information Processing Societies.
Anderson, J. A., C. D. Lorenz, and A. Travesset. 2008. “General purpose molecular dynamics simulations fully implemented on graphics processing units.” J. Comput. Phys. 227 (10): 5342–5359. https://doi.org/10.1016/j.jcp.2008.01.047.
Appleyard, J., and D. Drikakis. 2011. “Higher-order CFD and interface tracking methods on highly-parallel MPI and GPU systems.” Comput. Fluids 46 (1): 101–105. https://doi.org/10.1016/j.compfluid.2010.10.019.
Bartezzaghi, A., M. Cremonesi, N. Parolini, and U. Perego. 2015. “An explicit dynamics GPU structural solver for thin shell finite elements.” Comput. Struct. 154 (Jul): 29–40. https://doi.org/10.1016/j.compstruc.2015.03.005.
Bathe, K. J. 1996. Finite element procedures. 1st ed. Upper Saddle River, NJ: Prentice Hall.
Baugh, J. W., Jr., and S. K. Sharma. 1994. “Evaluation of distributed finite element algorithms on a workstation network.” Eng. Comput. 10 (1): 45–62. https://doi.org/10.1007/BF01206539.
Beckingsale, D. A., J. Burmark, R. Hornung, H. Jones, W. Killian, A. J. Kunen, O. Pearce, P. Robinson, B. S. Ryujin, and T. R. W. Scogland. 2019. “RAJA: Portable performance for large-scale scientific applications.” In Proc., 2019 IEEE/ACM Int. Workshop on Performance, Portability and Productivity in HPC (P3HPC). New York: IEEE. https://doi.org/10.1109/P3HPC49587.2019.00012.
Beisheim, J. 2010. “Speed up simulations with a GPU.” In ANSYS Advantage, 6–8. Canonsburg, PA: ANSYS.
Berger, P., P. Brouaye, and J. C. Syre. 1982. “A mesh coloring method for efficient MIMD processing in finite element problems.” In Proc., of the Int. Conf. on Parallel Processing, ICPP’82, 41–46. Washington, DC: IEEE Computer Society.
Berry, M. W., and R. J. Plemmons. 1987. “Algorithms and experiments for structural mechanics on high-performance architectures.” Comput. Methods Appl. Mech. Eng. 64 (1–3): 487–507. https://doi.org/10.1016/0045-7825(87)90052-1.
Bolz, J., I. Farmer, E. Grinspun, and P. Schrooder. 2003. “Sparse matrix solvers on the GPU: Conjugate gradients and multigrid.” In Proc., ACM SIGGRAPH 2003 Papers, 917–924. New York: Association for Computing Machinery.
Borkar, S., P. Dubey, K. Kahn, D. Kuck, H. Mulder, S. Pawlowski, and J. Rattner. 2005. “Platform 2015: Intel processor and platform evolution for the next decade.” In Intel White Paper, 30–36. Santa Clara, CA: Intel.
Brandvik, T., and G. Pullan. 2007. “Acceleration of a two-dimensional Euler flow solver using commodity graphics hardware.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 221 (12): 1745–1748. https://doi.org/10.1243/09544062JMES813FT.
Brown, J., V. Barra, N. Beams, L. Ghaffari, M. Knepley, W. Moses, R. Shakeri, K. Stengel, J. Thompson, and J. Zhang. 2022. “Performance portable solid mechanics via matrix-free p-multigrid.” Preprint, submitted April 4, 2022. https://arxiv.org/abs/2204.01722.
Brussino, G., and V. Sonnad. 1989. “A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations.” Int. J. Numer. Methods Eng. 28 (4): 801–815. https://doi.org/10.1002/nme.1620280406.
Buatois, L., G. Caumon, and B. Levy. 2007. “Concurrent number cruncher: An efficient sparse linear solver on the GPU.” In Proc., Int. Conf. on High Performance Computing and Communications, 358–371. Berlin: Springer.
Byna, S., M. S. Breitenfeld, B. Dong, Q. Koziol, E. Pourmal, D. Robinson, J. Soumagne, H. Tang, V. Vishwanath, and R. Warren. 2020. “ExaHDF5: Delivering efficient parallel I/O on exascale computing systems.” J. Comput. Sci. Technol. 35 (1): 145–160. https://doi.org/10.1007/s11390-020-9822-9.
Cai, Y., G. Li, H. Wang, G. Zheng, and S. Lin. 2012. “Development of parallel explicit finite element sheet forming simulation system based on GPU architecture.” Adv. Eng. Software 45 (1): 370–379. https://doi.org/10.1016/j.advengsoft.2011.10.014.
Cai, Y., G. Wang, G. Li, and H. Wang. 2015. “A high performance crashworthiness simulation system based on GPU.” Adv. Eng. Software 86 (Aug): 29–38. https://doi.org/10.1016/j.advengsoft.2015.04.003.
Carey, G. F., E. Barragy, R. McLay, and M. Sharma. 1988. “Element-by-element vector and parallel computations.” Commun. Appl. Numer. Methods 4 (3): 299–307. https://doi.org/10.1002/cnm.1630040303.
Cecka, C., A. Lew, and E. Darve. 2011. “Assembly of finite element methods on graphics processors.” Int. J. Numer. Methods Eng. 85 (5): 640–669. https://doi.org/10.1002/nme.2989.
Cevahir, A., A. Nukada, and S. Matsuoka. 2010. “High performance conjugate gradient solver on multi-GPU clusters using hypergraph partitioning.” Comput. Sci.-Res. Dev. 25 (1–2): 83–91. https://doi.org/10.1007/s00450-010-0112-6.
Che, S., M. Boyer, J. Meng, D. Tarjan, J. W. Sheaffer, and K. Skadron. 2008. “A performance study of general-purpose applications on graphics processors using CUDA.” J. Parallel Distrib. Comput. 68 (10): 1370–1380. https://doi.org/10.1016/j.jpdc.2008.05.014.
Chen, W., Y. Zhu, F. Cui, L. Liu, Z. Sun, J. Chen, and Y. Li. 2016. “GPU-accelerated molecular dynamics simulation to study liquid crystal phase transition using coarse-grained Gay-Berne anisotropic potential.” PloS one 11 (3): e0151704. https://doi.org/10.1371/journal.pone.0151704.
Corrigan, A., F. F. Camelli, R. Löhner, and J. Wallin. 2011. “Running unstructured grid-based CFD solvers on modern graphics hardware.” Int. J. Numer. Methods Fluids 66 (2): 221–229. https://doi.org/10.1002/fld.2254.
Courtecuisse, H., H. Jung, J. Allard, C. Duriez, D. Y. Lee, and S. Cotin. 2010. “GPU-based real-time soft tissue deformation with cutting and haptic feedback.” Prog. Biophys. Mol. Biol. 103 (2–3): 159–168. https://doi.org/10.1016/j.pbiomolbio.2010.09.016.
Crivelli, L., and M. Dunbar. 2012. “Evolving use of GPU for Dassault Systemes simulation products.” In Proc., GPU Technology Conf. (GTC 2012. San Jose, CA: NVIDIA.
Cui, Y., et al. 2013. “Physics-based seismic hazard analysis on petascale heterogeneous supercomputers.” In Proc., SC’13: Proc. of the Int. Conf. on High Performance Computing, Networking, Storage and Analysis. New York: IEEE.
Curtis, N. J., K. E. Niemeyer, and C.-J. Sung. 2017. “An investigation of GPU-based stiff chemical kinetics integration methods.” Combust. Flame 179 (May): 312–324. https://doi.org/10.1016/j.combustflame.2017.02.005.
Dalrymple, R. A., A. Hérault, G. Bilotta, and R. J. Farahani. 2010. “GPU-accelerated SPH model for water waves and free surface flows.” In Proc., of the Coastal Engineering Conf. Reston, VA: ASCE.
Demidov, D. 2019. “AMGCL: An efficient, flexible, and extensible algebraic multigrid implementation.” Lobachevskii J. Math. 40: 535–546. https://doi.org/10.1134/S1995080219050056.
Dokainish, M. A., and K. Subbaraj. 1989. “A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods.” Comput. Struct. 32 (6): 1371–1386. https://doi.org/10.1016/0045-7949(89)90314-3.
Dziekonski, A., P. Sypek, A. Lamecki, and M. Mrozowski. 2012. “Finite element matrix generation on a GPU.” Prog. Electromagn. Res. 128 (Apr): 249–265. https://doi.org/10.2528/PIER12040301.
Elgamal, A., L. Yan, Z. Yang, and J. P. Conte. 2008. “Three-dimensional seismic response of Humboldt Bay bridge-foundation-ground system.” J. Struct. Eng. 134 (7): 1165–1176. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:7(1165).
El-Sayad, M. E. M., and C.-K. Hsiung. 1990. “Parallel finite element computation with separate substructures.” Comput. Struct. 36 (2): 261–265. https://doi.org/10.1016/0045-7949(90)90125-L.
Farhat, C. 1990. “Which parallel finite element algorithm for which architecture and which problem?” Eng. Comput. 7 (3): 186–195. https://doi.org/10.1108/eb023805.
Farhat, C., and L. Crivelli. 1989. “A general approach to nonlinear FE computations on shared-memory multiprocessors.” Comput. Methods Appl. Mech. Eng. 72 (2): 153–171. https://doi.org/10.1016/0045-7825(89)90157-6.
Farhat, C., E. Wilson, and G. Powell. 1987. “Solution of finite element systems on concurrent processing computers.” Eng. Comput. 2 (3): 157–165. https://doi.org/10.1007/BF01201263.
FEMA. 1996. Performance based seismic design of buildings: An action plan for future studies. FEMA 283. Washington, DC: FEMA.
Filipovic, J., I. Peterlik, and J. Fousek. 2009. “GPU acceleration of equations assembly in finite elements method—Preliminary results.” In Proc., Symp. on Application Accelerators in HPC (SAAHPC). Urbana, IL: US National Center for Supercomputing Applications.
Foley, C. M., and S. Vinnakota. 1994. “Parallel processing in the elastic nonlinear analysis of high-rise frameworks.” Comput. Struct. 52 (6): 1169–1179. https://doi.org/10.1016/0045-7949(94)90183-X.
Fu, Z., T. J. Lewis, R. M. Kirby, and R. T. Whitaker. 2014. “Architecting the finite element method pipeline for the GPU.” J. Comput. Appl. Math. 257 (Feb): 195–211. https://doi.org/10.1016/j.cam.2013.09.001.
Garland, M., and D. B. Kirk. 2010. “Understanding throughput-oriented architectures.” Commun. ACM 53 (11): 58–66. https://doi.org/10.1145/1839676.1839694.
Georgescu, S., P. Chow, and H. Okuda. 2013. “GPU Acceleration for FEM-based structural analysis.” Arch. Comput. Methods Eng. 20 (2): 111–121. https://doi.org/10.1007/s11831-013-9082-8.
Georgescu, S., and H. Okuda. 2010. “Conjugate gradients on multiple GPUs.” Int. J. Numer. Methods Fluids 64 (10–12): 1254–1273. https://doi.org/10.1002/fld.2462.
Geveler, M., D. Ribbrock, D. Gdeke, P. Zajac, and S. Turek. 2011. “Efficient finite element geometric multigrid solvers for unstructured grids on GPUs.” In Proc., 2nd Int. Conf. on Parallel, Distributed, Grid and Cloud Computing for Engineering (PARENG 2011). Corsica, France: Civil-Comp.
Ghattas, O. 2011. “Uncertainty quantification and exascale computing: Opportunities and challenges for earthquake engineering.” In Proc., Grand Challenges in Earthquake Engineering Research: A Community Workshop Report, 74–80. Washington DC: National Research Council of the National Academies.
Gimenez, J. M., D. E. Ramajo, S. Márquez Damián, N. M. Nigro, and S. R. Idelsohn. 2017. “An assessment of the potential of PFEM-2 for solving long real-time industrial applications.” Comput. Part. Mech. 4 (3): 251–267. https://doi.org/10.1007/s40571-016-0135-2.
Goddeke, D., R. Strzodka, and S. Turek. 2007. “Performance and accuracy of hardware-oriented native-, emulated- and mixed-precision solvers in FEM simulations.” Int. J. Parallel Emergent Distrib. Syst. 22 (4): 221–256. https://doi.org/10.1080/17445760601122076.
Gohner, U. 2012. “Usage of GPU in LS-DYNA.” In Proc., LS-DYNA Forum. Stuttgart, Germany: DYNAmore.
Gorobets, A., and P. Bakhvalov. 2022. “Heterogeneous CPU+GPU parallelization for high-accuracy scale-resolving simulations of compressible turbulent flows on hybrid supercomputers.” Comput. Phys. Commun. 271 (Feb): 108231. https://doi.org/10.1016/j.cpc.2021.108231.
Govindaraju, N. K., and D. Manocha. 2007. “Cache-efficient numerical algorithms using graphics hardware.” Parallel Comput. 33 (10–11): 663–684. https://doi.org/10.1016/j.parco.2007.09.006.
Haase, G., M. Liebmann, C. C. Douglas, and G. Plank. 2010. “A parallel algebraic multigrid solver on graphics processing units.” In High performance computing and applications, 38–47. Berlin: Springer.
Hairer, E., and G. Wanner. 2012. Solving ordinary differential equations II: Stiff and differential-algebraic problems. Berlin: Springer-Verlag.
Hajjar, J. F., and J. F. Abel. 1988. “Parallel processing for transient nonlinear structural dynamics of three-dimensional framed structures using domain decomposition.” Comput. Struct. 30 (6): 1237–1254. https://doi.org/10.1016/0045-7949(88)90189-7.
Hérault, A., G. Bilotta, and R. A. Dalrymple. 2010. “SPH on GPU with CUDA.” Supplement, J. Hydraul. Res. 48 (S1): 74–79. https://doi.org/10.1080/00221686.2010.9641247.
Hughes, T. J. R. 1987. The finite element method. Englewood Cliffs, NJ: Prentice Hall.
Hughes, T. J. R., R. M. Ferencz, and J. O. Hallquist. 1987. “Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradients.” Comput. Methods Appl. Mech. Eng. 61 (2): 215–248. https://doi.org/10.1016/0045-7825(87)90005-3.
Inoue, N. 2015. “Speeding up a finite element computation on GPU.” In Proc., GPU Technology Conf. Silicon Valley, CA: NVIDIA.
Jeremic, B., and G. Jie. 2008. “Parallel soil–foundation–structure interaction computations.” In Computational structural dynamics and earthquake engineering. Boca Raton, FL: CRC Press.
Johnsen, S. F., et al. 2015. “NiftySim: A GPU-based nonlinear finite element package for simulation of soft tissue biomechanics.” Int. J. Comput. Assisted Radiol. Surg. 10 (7): 1077–1095. https://doi.org/10.1007/s11548-014-1118-5.
Joldes, G. R., A. Wittek, and K. Miller. 2010. “Real-time nonlinear finite element computations on GPU—Application to neurosurgical simulation.” Comput. Methods Appl. Mech. Eng. 199 (49–52): 3305–3314. https://doi.org/10.1016/j.cma.2010.06.037.
Kampolis, I. C., X. S. Trompoukis, V. G. Asouti, and K. C. Giannakoglou. 2010. “CFD-based analysis and two-level aerodynamic optimization on graphics processing units.” Comput. Methods Appl. Mech. Eng. 199 (9–12): 712–722. https://doi.org/10.1016/j.cma.2009.11.001.
Karatarakis, A., P. Karakitsios, and M. Papadrakakis. 2014. “GPU accelerated computation of the isogeometric analysis stiffness matrix.” Comput. Methods Appl. Mech. Eng. 269 (Feb): 334–355. https://doi.org/10.1016/j.cma.2013.11.008.
Kilic, S. A., F. Saied, and A. Sameh. 2004. “Efficient iterative solvers for structural dynamics problems.” Comput. Struct. 82 (28): 2363–2375. https://doi.org/10.1016/j.compstruc.2004.06.001.
Kim, T. 2008. “Hardware-aware analysis and optimization of ‘Stable fluids’.” In Proc., of the ACM Symp. on Interactive 3D Graphics and Games. New York: Association for Computing Machinery.
Kiran, U., D. Sharma, and S. S. Gautam. 2019. “GPU-warp based finite element matrices generation and assembly using coloring method.” J. Comput. Des. Eng. 6 (4): 705–718. https://doi.org/10.1016/j.jcde.2018.11.001.
Kirk, D. B., and W.-M. W. Hwu. 2013. Programming massively parallel processors: A hands-on approach. Waltham, MA: Morgan Kaufmann.
Klockner, A., T. Warburton, J. Bridge, and J. S. Hesthaven. 2009. “Nodal discontinuous Galerkin methods on graphics processors.” J. Comput. Phys. 228 (21): 7863–7882. https://doi.org/10.1016/j.jcp.2009.06.041.
Knepley, M. G., and A. R. Terrel. 2011. Finite element integration on GPUs. Austin, TX: Texas Advanced Computing Center.
Komatitsch, D., G. Erlebacher, D. Göddeke, and D. Michéa. 2010. “High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster.” J. Comput. Phys. 229 (20): 7692–7714. https://doi.org/10.1016/j.jcp.2010.06.024.
Komatitsch, D., D. Michéa, and G. Erlebacher. 2009. “Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA.” J. Parallel Distrib. Comput. 69 (5): 451–460. https://doi.org/10.1016/j.jpdc.2009.01.006.
Kothe, D., L. Diachin, A. Siegel, and E. Draeger. 2019. Application development update. Washington, DC: Exascale Computing Project.
Kraus, J., and M. Foster. 2012. “Efficient AMG on heterogeneous systems.” In Vol. 7174 of Facing the multicore—Challenge II, lecture notes in computer science, edited by R. Keller, D. Kramer, and J. P. Weiss, 133–146. Berlin: Springer.
Krawezik, G., and G. Poole. 2009. “Accelerating the ANSYS direct sparse solver with GPUs.” In Proc., 2009 Symp. on Application Accelerators in High Performance Computing (SAAHPC’09). Urbana, IL: US National Center for Supercomputing Applications.
Kruger, J., and R. Westermann. 2003. “Linear algebra operators for GPU implementation of numerical algorithms.” ACM Trans. Graphics 22 (3): 908–916. https://doi.org/10.1145/882262.882363.
Kumar, S., and H. Adeli. 1995. “Distributed finite-element analysis on network of workstations—Implementation and application.” J. Struct. Eng. 121 (10): 1456–1462. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:10(1456).
Kusakabe, R., K. Fujita, T. Ichimura, M. Hori, and L. Wijerathne. 2019. “A fast 3D finite-element solver for large-scale seismic soil liquefaction analysis.” In Vol. 11537 of Proc., Int. Conf. on Computational Science, Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 349–362. Cham, Switzerland: Springer.
Kusakabe, R., K. Fujita, T. Ichimura, T. Yamaguchi, M. Hori, and L. Wijerathne. 2021. “Development of regional simulation of seismic ground-motion and induced liquefaction enhanced by GPU computing.” Earthquake Eng. Struct. Dyn. 50 (1): 197–213. https://doi.org/10.1002/eqe.3369.
Kuznik, F., C. Obrecht, G. Rusaouen, and J.-J. Roux. 2010. “LBM based flow simulation using GPU computing processor.” Comput. Math. Appl. 59 (7): 2380–2392. https://doi.org/10.1016/j.camwa.2009.08.052.
Lacoste, X., P. Ramet, M. Faverge, Y. Ichitaro, and J. Dongarra. 2012. Sparse direct solvers with accelerators over DAG runtimes. Research Rep. RR-7972. Talence, France: INRIA Bordeaux.
Law, K. H. 1986. “A parallel finite element solution method.” Comput. Struct. 23 (6): 845–858. https://doi.org/10.1016/0045-7949(86)90254-3.
Leung, A., N. Vasilache, B. Meister, M. Baskaran, D. Wohlford, C. Bastoul, and R. Lethin. 2010. “A mapping path for multi-GPGPU accelerated computers from a portable high level programming abstraction.” In Proc., 3rd Workshop on General-Purpose Computation on Graphics Processing Units, 51–61. New York: Association for Computing Machinery.
Li, R., and Y. Saad. 2010. “GPU-accelerated preconditioned iterative linear solvers.” Technical Rep. Minneapolis: Univ. of Minnesota.
Lindstrom, P. 2014. “Fixed-rate compressed floating-point arrays.” IEEE Trans. Visual Comput. Graphics 20 (12): 2674–2683. https://doi.org/10.1109/TVCG.2014.2346458.
Liu, P., and V. Dinavahi. 2018. “Matrix-free nodal domain decomposition with relaxation for massively parallel finite-element computation of EM apparatus.” IEEE Trans. Magn. 54 (9): 1–7. https://doi.org/10.1109/TMAG.2018.2848622.
Ljungkvist, K. 2015. “Techniques for finite element methods on modern processors.” Ph.D. dissertation, Dept. of Information Technology, Uppsala Univ.
Lu, X., and H. Guan. 2017. Earthquake disaster simulation of civil infrastructures: From tall buildings to urban areas. Beijing: Science Press.
Luitjens, J., A. Williams, and M. Heroux. 2012. “Optimizing MiniFE an implicit nite element application on GPUs.” In Proc., GPU Technology Conf. (GTC 2012). Santa Clara, CA: NVIDIA.
Mackerle, J. 1996. “Implementing finite element methods on supercomputers, workstations and PCs: A bibliography (1985-1995).” Eng. Comput. 13 (1): 33–85. https://doi.org/10.1108/02644409610110985.
Mackerle, J. 2003. “FEM and BEM parallel processing: Theory and applications—A bibliography (1996-2002).” Eng. Comput. 20 (4): 436–484. https://doi.org/10.1108/02644400310476333.
Mackerle, J. 2004. “Object-oriented programming in FEM and BEM: A bibliography (1990-2003).” Adv. Eng. Software 35 (6): 325–336. https://doi.org/10.1016/j.advengsoft.2004.04.006.
Mafi, R. 2013. GPU-based parallel computing for nonlinear finite element deformation analysis. Hamilton, ON, Canada: McMaster Univ.
Mafi, R., and S. Sirouspour. 2014. “GPU-based acceleration of computations in nonlinear finite element deformation analysis.” Int. J. Numer. Methods Biomed. Eng. 30 (3): 365–381. https://doi.org/10.1002/cnm.2607.
Markall, G., A. Slemmer, D. Ham, P. Kelly, C. Cantwell, and S. Sherwin. 2013. “Finite element assembly strategies on multi-core and many-core architectures.” Int. J. Numer. Methods Fluids 71 (1): 80–97. https://doi.org/10.1002/fld.3648.
Martínez-Frutos, J., P. J. Martínez-Castejón, and D. Herrero-Pérez. 2015. “Fine-grained GPU implementation of assembly-free iterative solver for finite element problems.” Comput. Struct. 157 (Sep): 9–18. https://doi.org/10.1016/j.compstruc.2015.05.010.
McCallen, D., A. Petersson, A. Rodgers, A. Pitarka, M. Miah, F. Petrone, B. Sjogreen, N. Abrahamson, and H. Tang. 2021a. “EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers part I: Computational models and workflow.” Earthquake Spectra 37 (2): 707–735. https://doi.org/10.1177/8755293020970982.
McCallen, D., F. Petrone, M. Miah, A. Pitarka, A. Rodgers, and N. Abrahamson. 2021b. “EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers, Part II: Regional simulations of building response.” Earthquake Spectra 37 (2): 736–761. https://doi.org/10.1177/8755293020970980.
McCallen, D., H. Tang, S. Wu, E. Eckert, J. Huang, and N. A. Petersson. 2022. “Coupling of regional geophysics and local soil-structure models in the EQSIM fault-to-structure earthquake simulation framework.” Int. J. High Perform. Comput. Appl. 36 (1): 78–92. https://doi.org/10.1177/10943420211019118.
McKenna, F. 1997. Object-oriented finite element programming: Frameworks for analysis, algorithms and parallel computing. Berkeley, CA: Univ. of California.
McKenna, F., M. H. Scott, and G. L. Fenves. 2010. “Nonlinear finite-element analysis software architecture using object composition.” J. Comput. Civ. Eng. 24 (1): 95–107. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000002.
Mihaila, B., M. Knezevic, and A. Cardenas. 2014. “Three orders of magnitude improved efficiency with high-performance spectral crystal plasticity on GPU platforms.” Int. J. Numer. Methods Eng. 97 (11): 785–798. https://doi.org/10.1002/nme.4592.
Mills, R. T., et al. 2021. “Toward performance-portable PETSc for GPU-based exascale systems.” Parallel Comput. 108 (2021): 102831. https://doi.org/10.48550/arXiv.2011.00715.
Motley, M. R., H. K. Wong, X. Qin, A. O. Winter, and M. O. Eberhard. 2016. “Tsunami-induced forces on skewed bridges.” J. Waterway, Port, Coastal, Ocean Eng. 142 (3): 04015025. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000328.
Naumov, M., et al. 2015. “AmgX: A library for GPU accelerated algebraic multigrid and preconditioned iterative methods.” SIAM J. Sci. Comput. 37 (5): S602–S626. https://doi.org/10.1137/140980260.
Neic, A., M. Liebmann, and G. Haase. 2012. “Algebraic multigrid solver on clusters of CPUs and GPUs.” In Proc., Int. Workshop on Applied Parallel and Scienti c Computing, 389–398. Berlin: Springer.
Newmark, N. 1959. “A method of computation for structural dynamics.” J. Eng. Mech. Div. 85 (3): 67–94. https://doi.org/10.1061/JMCEA3.0000098.
NVIDIA. 2007. Compute unified device architecture programming guide. Santa Clara, CA: NVIDIA.
NVIDIA. 2012. PhysX. Santa Clara, CA: NVIDIA.
NVIDIA. 2013. NVIDIA CUDA C programming guide. Santa Clara, CA: NVIDIA.
NVIDIA. 2014. CuSP. Santa Clara, CA: NVIDIA.
NVIDIA. 2015. GPU-accelerated applications. Santa Clara, CA: NVIDIA.
NVIDIA. 2019. CUDA C best practices guide (v5.0). Santa Clara, CA: NVIDIA.
Nyland, L., M. Harris, and J. Prins. 2007. “Fast N-body simulation with CUDA.” In GPU Gems 3, 677–695. Boston: Addison-Wesley.
O’Reilly, O., T.-Y. Yeh, K. B. Olsen, Z. Hu, A. Breuer, D. Roten, and C. A. Goulet. 2022. “A high-order finite-difference method on staggered curvilinear grids for seismic wave propagation applications with topography.” Bull. Seismol. Soc. Am. 112 (1): 3–22. https://doi.org/10.1785/0120210096.
O’Rourke, T. D. 2010. “Geohazards and large, geographically distributed systems.” Géotechnique 60 (7): 505–543. https://doi.org/10.1680/geot.2010.60.7.505.
Owens, J. D., D. Luebke, N. Govindaraju, M. Harris, J. Krüger, A. E. Lefohn, and T. J. Purcell. 2005. “A survey of general-purpose computation on graphics hardware.” Comput. Graphics Forum 26 (1): 80–113. https://doi.org/10.1111/j.1467-8659.2007.01012.x.
Papadrakakis, M., G. Stavroulakis, and A. Karatarakis. 2011. “A new era in scientific computing: Domain decomposition methods in hybrid CPU-GPU architectures.” Comput. Methods Appl. Mech. Eng. 200 (13–16): 1490–1508. https://doi.org/10.1016/j.cma.2011.01.013.
Peterson, B., A. Humphrey, J. Holmen, T. Harman, M. Berzins, D. Sunderland, and H. C. Edwards. 2018. “Demonstrating GPU code portability and scalability for radiative heat transfer computations.” J. Comput. Sci. 27 (Jul): 303–319. https://doi.org/10.1016/j.jocs.2018.06.005.
Posey, S., and F. Courteille. 2012. “GPU progress in sparse matrix solvers for applications in computational mechanics.” In Vol. ESCO12 of Proc., European Seminar on Computing. Reston, VA: American Institute of Aeronautics and Astronautics.
Roa, M., K. Logarathan, and N. V. Raman. 1994. “Multi-frontal based approach for concurrent finite element analysis.” Comput. Struct. 52 (4): 841–846. https://doi.org/10.1016/0045-7949(94)90364-6.
Roten, D., Y. Cui, K. Olsen, S. Day, K. Withers, W. Savran, P. Wang, and D. Mu. 2016. “High-frequency nonlinear earthquake simulations on petascale heterogeneous supercomputers.” In Proc., SC’16 Proc. Supercomputing Conf. New York: IEEE.
Rumpf, M., and R. Strzodka. 2005. “Numerical solution of partial differential equations on parallel computers.” In Vol. 51 of Lecture notes in computational science and engineering, edited by A. M. Bruaset and A. Tveito, 89–134. Berlin: Springer.
Santiago, E. D., and K. H. Law. 1996. “An implementation of finite element method on distributed workstations.” In Proc., Analysis and Computation: Proc. of the Twelfth Conf. Held in Conjunction with Structures Congress XIV, edited by F. Y. Cheng, 188–199. Reston, VA: ASCE.
Schenk, O., M. Christen, and H. Burkhart. 2008. “Algorithmic performance studies on graphics processing units.” J. Parallel Distrib. Comput. 68 (10): 1360–1369. https://doi.org/10.1016/j.jpdc.2008.05.008.
Sharma, G., A. Agarwala, and B. Bhattacharya. 2013. “A fast parallel Gauss Jordan algorithm for matrix inversion using CUDA.” Comput. Struct. 128 (Nov): 31–37. https://doi.org/10.1016/j.compstruc.2013.06.015.
Siegel, A., E. Draeger, J. Deslippe, A. Dubey, T. Evans, T. Germann, and W. Hart. 2020. Early application results on pre-exascale architecture with analysis of performance challenges and projections. Washington, DC: Exascale Computing Project.
Snell, A., and L. Segervall. 2017. HPC application support for GPU computing. Sunnyvale, CA: Intersect 360 Research: Accurate Market Intelligence for High Performance Computing.
Stone, C. P., and R. L. Davis. 2013. “Techniques for solving stiff chemical kinetics on graphical processing units.” J. Propul. Power 29 (4): 764–773. https://doi.org/10.2514/1.B34874.
Sunarso, A., T. Tsuji, and S. Chono. 2010. “GPU-accelerated molecular dynamics simulation for study of liquid crystalline flows.” J. Comput. Phys. 229 (15): 5486–5497. https://doi.org/10.1016/j.jcp.2010.03.047.
Sutter, H. 2005. “The free lunch is over: A fundamental turn toward concurrency in software.” Dr. Dobb’s J. 30 (3): 202–210.
Sylwestrzak, M., D. Szlag, P. J. Marchand, A. S. Kumar, and T. Lasser. 2017. “Massively parallel data processing for quantitative total flow imaging with optical coherence microscopy and tomography.” Comput. Phys. Commun. 217 (Aug): 128–137. https://doi.org/10.1016/j.cpc.2017.03.008.
Synn, S. Y., and R. E. Fulton. 1995. “Practical strategy for concurrent substructure analysis.” Comput. Struct. 54 (5): 939–944. https://doi.org/10.1016/0045-7949(94)00385-G.
Tavakkol, S., and P. Lynett. 2017. “Celeris: A GPU-accelerated open source software with a Boussinesq-type wave solver for real-time interactive simulation and visualization.” Comput. Phys. Commun. 217 (Aug): 117–127. https://doi.org/10.1016/j.cpc.2017.03.002.
Taylor, Z., M. Cheng, and S. Ourselin. 2008. “High-speed nonlinear finite element analysis for surgical simulation using graphics processing units.” IEEE Trans. Med. Imaging 27 (5): 650–663. https://doi.org/10.1109/TMI.2007.913112.
Tian, Y., L. Xie, Z. Xu, and X. Lu. 2015. “GPU-powered high-performance computing for the analysis of large-scale structures based on OpenSees.” In Proc., ASCE Computing in Civil Engineering, 411–418. Reston, VA: ASCE.
Ting, E. C., C. Shih, and Y.-K. Wang. 2004. “Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame element.” J. Mech. 20 (2): 113–122. https://doi.org/10.1017/S1727719100003336.
Tomov, S., J. Dongarra, and M. Baboulin. 2010. “Towards dense linear algebra for hybrid GPU accelerated manycore systems.” Parallel Comput. 36 (5–6): 232–240. https://doi.org/10.1016/j.parco.2009.12.005.
Topping, B. H., and A. I. Khan. 1996. Parallel finite element computations. Edinburgh, UK: Saxe-Coburg Publications.
Verschoor, M., and A. C. Jalba. 2012. “Analysis and performance estimation of the conjugate gradient method on multiple GPUs.” Parallel Comput. 38 (10–11): 552–575. https://doi.org/10.1016/j.parco.2012.07.002.
Wagner, M., K. Rupp, and J. Weinbub. 2012. “A comparison of algebraic multigrid preconditioners using graphics processing units and multi-core central processing units.” In Vol. 2 of Proc., 2012 Symp. on High Performance Computing, HPC ’12, 1–8. San Diego: Society for Computer Simulation International.
Wang, M., H. Klie, M. Parashar, and H. Sudan. 2009. “Solving sparse linear systems on NVIDIA Tesla GPUs.” In Proc., Computational Science (ICCS 2009), 864–873. Cham, Switzerland: Springer Nature.
Yamaguchi, T., K. Fujita, T. Ichimura, A. Naruse, M. Lalith, and M. Hori. 2020. “GPU implementation of a sophisticated implicit low-order finite element solver with FP21-32-64 computation using OpenACC.” In Vol. 12017 of Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), 3–24. Cham, Switzerland: Springer.
Yang, Y.-S., C.-M. Yang, and T.-J. Hsieh. 2014. “GPU parallelization of an object-oriented nonlinear dynamic structural analysis platform.” Simul. Modell. Pract. Theory 40 (Jan): 112–121. https://doi.org/10.1016/j.simpat.2013.09.004.
Zhang, W., and E. M. Lui. 1991. “A parallel frontal solver on the Alliant FX/80.” Comput. Struct. 38 (2): 203–215. https://doi.org/10.1016/0045-7949(91)90097-6.
Zhou, H., G. Mo, F. Wu, J. Zhao, M. Rui, and K. Cen. 2012. “GPU implementation of lattice Boltzmann method for flows with curved boundaries.” Comput. Methods Appl. Mech. Eng. 225 (Jun): 65–73. https://doi.org/10.1016/j.cma.2012.03.011.
Zhou, J., Y. Cui, E. Poyraz, D. J. Choi, and C. C. Guest. 2013. “Multi-GPU implementation of a 3D finite difference time domain earthquake code on heterogeneous supercomputers.” Procedia Comput. Sci. 18 (Jan): 1255–1264. https://doi.org/10.1016/j.procs.2013.05.292.
Zhu, M., and M. H. Scott. 2014. “Modeling fluid–structure interaction by the particle finite element method in OpenSees.” Comput. Struct. 132 (Feb): 12–21. https://doi.org/10.1016/j.compstruc.2013.11.002.
Zienkiewicz, O. C., and R. L. Taylor. 1989. The finite element method. London: McGraw-Hill.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 149Issue 3March 2023

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Received: Jan 21, 2022
Accepted: Aug 24, 2022
Published online: Dec 22, 2022
Published in print: Mar 1, 2023
Discussion open until: May 22, 2023

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Assistant Professor, School of Civil and Environmental Engineering, Stanford Univ., Stanford, CA 94305 (corresponding author). ORCID: https://orcid.org/0000-0002-3661-9548. Email: [email protected]
Minjie Zhu, Ph.D. [email protected]
Research Associate, School of Civil and Construction Engineering, Oregon State Univ., Corvallis, OR 97331. Email: [email protected]
Graduate Student Researcher, School of Civil and Environmental Engineering, Stanford Univ., Stanford, CA 94305. ORCID: https://orcid.org/0000-0002-7736-7375. Email: [email protected]
Professor, School of Civil and Construction Engineering, Oregon State Univ., Corvallis, OR 97331. ORCID: https://orcid.org/0000-0001-5898-5090. Email: [email protected]

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